Emory Erickson, inventor of the transporter, denounced questioning if the person who arrived after a transport was the same person who left as "metaphysical chatter." (ENT: "Daedalus")

In 2266, Captain Kirk of the USS Enterprise engaged the supercomputer Landru in a metaphysical debate. Landru regarded itself as an exact copy of its maker, an ancient philosopher and engineer. Kirk exploited certain key differences between the creator and the created to set up a paradox that the machine could not resolve. These limitations, rooted in its understanding of the world and of itself, had prevented it from realizing the harm it was doing to the citizens of Beta III, in direct violation of its programming. They also prevented it from deducing a way to resolve that harm, and ultimately, it experienced catastrophic failure. (TOS: "The Return of the Archons")